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arXiv · 1408.0538

On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model

Ilia Binder·Michael Goldstein·Mircea Voda
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Abstract

We provide an explicit lower bound for the the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model. In particular, for the Anderson model on a strip of width $ W $ the lower bound is proportional to $ W^{-ε} $, for any $ ε>0 $. This bound is consistent with the fact that the lowest non-negative Lyapunov exponent is conjectured to have a lower bound proportional to $ W^{-1} $.

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Ilia Binder, Michael Goldstein, Mircea Voda. 2014-08-03. On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model. https://doi.org/10.1017/etds.2015.59

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